A geometric criterion for Gelfand pairs associated with the Heisenberg group

DOI10.2140/pjm.1997.178.1zbMath0868.22015OpenAlexW2101545272MaRDI QIDQ1816498

Gail Ratcliff, Chal Benson, Ronald L. Lipsman, J. W. Jenkins

Publication date: 15 December 1996

Published in: Pacific Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2140/pjm.1997.178.1

zbMATH Keywords

Heisenberg groupGelfand pairorbit methodintegral coadjoint orbits

Mathematics Subject Classification ID

Analysis on real and complex Lie groups (22E30) Summability methods on groups, semigroups, etc. (43A55)

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Branching rule and coadjoint orbit for Heisenberg Gelfand pairs ⋮ Geometric models for the spectra of certain Gelfand pairs associated with Heisenberg groups ⋮ A unified approach to concrete Plancherel theory of homogeneous spaces ⋮ The moment map for a multiplicity free action ⋮ Corwin–Greenleaf multiplicity function for compact extensions of the Heisenberg group ⋮ An orbit model for the spectra of nilpotent Gelfand pairs ⋮ Classification of skew multiplicity-free modules. ⋮ Dual topology of the motion groups ⋮ The space of bounded spherical functions on the free 2-step nilpotent Lie group ⋮ Gelfand pairs attached to representations of compact Lie groups ⋮ A geometric criterion for Gelfand pairs associated with nilpotent Lie groups ⋮ Gelfand pairs on the Heisenberg group and Schwartz functions ⋮ The Penney-Fujiwara Plancherel formula for Gelfand pairs ⋮ The orbit method and Gelfand pairs, associated with nilpotent Lie groups ⋮ Spaces of bounded spherical functions on Heisenberg groups. I ⋮ Spaces of bounded spherical functions on Heisenberg groups. II ⋮ Orbit method and dual topology for certain Lie groups ⋮ Coherent states and Berezin quantization for non-scalar holomorphic representations ⋮ Spherical nilpotent orbits and the Kostant-Sekiguchi correspondence

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